%%%% show various distance metrics using the pdisp matlab function

new;

d = 7;
scalinglimits=[1 8];
a = round( scale( rand(d+1,3), scalinglimits) * 10) / 10
d = min( d, size( a, 1)-1);

d1=pdist(a,'minkowski',4);
d1=d1(1:d)
d2=pdist(a,'cityblock');
d2=d2(1:d)
d3=pdist(a,'euclidean');
d3=d3(1:d)
d4=pdist(a,'mahalanobis');
d4=d4(1:d)
d5=pdist(a,'chebychev');
d5=d5(1:d)

figure;
set( gcf,'name','Distances example');
subplot(121);
imagesc( a); colormap gray; colorbar; axis image;
set( gca, 'XTick',1:1:3);
xlabel('variables');
ylabel('observations');
title('visualization of input data');
set(gca,'Visible','on');
subplot(122);
plot(1:d,d1,'ko',1:d,d2,'bs',1:d,d3,'g^',1:d,d4,'rd',1:d,d5,'m<','LineWidth',3,'MarkerSize',10);
set( gca, 'XTick',1:1:d);
xlabel('comparison');
ylabel('distance');
title('Different distance metrics');
legend('Minkowski 4','Cityblock','Euclidean','Mahalanobis','Chebychev','Location','NW');
axis tight; 
grid on;